Final answer:
The domain of the function g(x)=sqrt(6−x) is all x-values less than or equal to 6, and the domain of the function g(x)=sqrt(2−x) is all x-values less than or equal to 2.
Step-by-step explanation:
To find the domain of the function g(x)=sqrt(6−x) and g(x)=sqrt(2−x), we need to consider the properties of the square root function. The square root is real only for positive values and zero, so the expression inside the square root, also known as the radicand, must be greater than or equal to zero.
For g(x)=sqrt(6−x), the domain would be the set of all x such that 6 - x ≥ 0. By solving this inequalities, we find that x ≤ 6. Therefore the domain is all x-values less than or equal to 6.
Similarly, for g(x)=sqrt(2−x), the domain would be the set of all x such that 2 - x ≥ 0. By solving this inequalities, we find that x ≤ 2. Therefore the domain is all x-values less than or equal to 2.
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